Droplets with interfacial viscosity: dynamics, rheology, and breakup

In this talk, we discuss the dynamics of droplets with a thin layer of viscous, insoluble surfactant whose mechanics are described by interfacial viscosity, i.e., a Boussinesq-Scriven constitutive law. We develop analytical theories to quantify droplet shape under flow in the limit of weak deformation, to a sufficient level of approximation where one can extract information about non-linear rheology and droplet breakup. In shear flow and extensional flows, we calculate how interfacial viscosity alters the extra stress of a dilute suspension of droplets. We also investigate how shear and dilatational viscosities influence droplet breakup and droplet migration in wall-bounded shear flow. These theories highlight the extent to which surface viscosity alters droplet dynamics, and we discuss how one can extend our theories to include effects such as surface tension gradients and viscoelastic surfaces. In the last part of the talk, we discuss a peculiar result that is related to the translational speed of a droplet with interfacial viscosity.  It turns out interfacial shear viscosity plays a minimal role in modifying droplet drag when its shape is spherical.  We discuss physical mechanisms and scaling theories that explain this observation.